A waveguide crossing includes a first waveguide and a second waveguide intersecting the first waveguide such that a gap equal to a width of the second waveguide is formed in the first waveguide, the second waveguide having a centerline defining a plane of symmetry. The first waveguide has a first waveguide section through which a single optical mode propagates, followed by a first non-adiabatic diverging taper, followed by a second waveguide section wider than the first waveguide section through which two even-order optical modes propagate, followed by a second non-adiabatic diverging taper, followed by a third waveguide section wider than the second waveguide section through which three even-order optical modes propagate. The three even-order modes synthesize to form a quasi-Gaussian beam that self-replicates symmetrically across the gap, thereby providing a low-loss waveguide crossing useful for photonic switching.